A particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant. Based on the information given, which of the following is true?

1.	The velocity and acceleration, both are parallel to \(r.\)
2.	The velocity is perpendicular to \(r\) and acceleration is directed towards the origin.
3.	The velocity is not perpendicular to \(r\) and acceleration is directed away from the origin.
4.	The velocity and acceleration, both are perpendicular to \(r.\)

A particle of mass 10g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8x10^-4 J by the end of the second revolution after the beginning of the motion?

1. 0.15 m/s²

2. 0.18 m/s²

3. 0.2 m/s²

4. 0.1 m/s²

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be 

1. $\frac{t_1-t_2}{2}$

2. $\frac{t_1{t}_2}{t_2-t_1}$

3. $\frac{t_1{t}_2}{t_2+t_1}$

4. $t_1-t_2$

In the given figure, \(a=15\) m/s² represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R=2.5\) m at a given instant of time. The speed of the particle is:
              

1. \(4.5\) m/s
2. \(5.0\) m/s
3. \(5.7\) m/s
4. \(6.2\) m/s

The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^2\) and \({y}=10{t}\) respectively, where \(x\) and \(y\) are in meters and \(\mathrm{t}\) in seconds. The acceleration of the particle at \(\mathrm{t}=2\) s is: